What is the vertex form of #x= 10y^2-31y+15 #?

1 Answer
Zack M.
Feb 1, 2016

The vertex form for a parabola is a function of the form;

#x=a(y-h)^2+k#

Where #(h,k)# is the vertex of the parabola. To convert a quadratic to vertex form, we want to start by isolating the #y# terms and completing the square.

#x=10(y^2-31/10 y)+ 15#

Complete the square inside the parenthesis.

#x=10(y^2-31/10 y + 961/400 - 961/400) + 15#

#x=10(y^2-31/10 y + 961/400) - 961/40 + 15#

#x=10(y^2-31/20)^2 - 24 1/400 + 15#

#x=10(y^2-31/20)^2 - 9 1/400 #

This is the vertex form of the equation.

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